A note on the flow time and the number of tardy jobs in stochastic open shops |
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Authors: | Michael Pinedo |
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Institution: | Department of Industrial Engineering and Operations Research, Columbia University, Seeley W. Mudd Building, New York, NY 10027, U.S.A. |
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Abstract: | In this note open shops with two machines are considered. The processing time of job j, j = 1, …, n, on machine 1 (2) is a random variable Xj (Yj), which is exponentially distributed with rate γ (μ). If the completion time of job j is Cj, a waiting cost is incurred of g(Cj), where g is a function that is increasing concave. The preemptive policy that minimizes the total expected waiting cost E(Σg(Cj)) is determined. Two machine open shops with jobs that have random due dates are considered as well. For the case where the due dates D1,…,Dn are exchangeable, the preemptive policy that minimizes the expected number of tardy jobs is determined. |
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Keywords: | Stochastic scheduling exponential distribution job shop |
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